Search for the missing cone

[jbtsax]

I have undertaken a study to investigate ways to calculate the so called "missing cone" of the saxophone that the volume of the mouthpiece is supposed to substitute in order for the sax to play properly.

The findings of the study are at this link: http://jbtsaxmusic.homestead.com/Missing_Cone_Volume_Comparison_Study.pdf

It is important to note that this is just one saxophone neck and one mouthpiece. Further tests are needed before any general conclusions can be drawn that apply to all sizes, makes, and models of saxophone and mouthpieces.

Two related studies are: http://jbtsaxmusic.homestead.com/Detailed_SBA_neck_measurements.pdf and http://jbtsaxmusic.homestead.com/mouthpiece_equivalent_volume_study.pdf

John

[MartinMods]

Hi John,

I have some questions about the figured mouthpiece equivalent volume.

In your MEV study the MEV added 2.78cc or 28% to the physical mouthpiece chamber volume used.

In your MCV study, MEV added only 1.28cc or 18.63% to the physical mouthpiece chamber volume used.

The same mouthpiece was used for both tests.

Benade's conclusions to his similar MEV study showed that the MEV was quite constant over a considerable portion of the instrument's range. Understandable since, also being termed "reed compliance" one might see it as a property of the reed and the mouthpiece facing, rather than the changing mouthpiece chamber volume (used) and tube air column length.

Can you explain how you were able to get from 28% in the first study to 18.63% in the second study?

[pete]

I have a couple questions, too:

* First, wouldn't a straight soprano with a fixed neck be easier to work with, like, a Mark VI? You wouldn't have to worry about the neck as a measurement or any bends. (Of course, if you had the measurements from another source, just disregard this comment.)

* Second, don't the tone holes do something to the overall volume of the cone or is that included in the measurements?

* Third, do you really want a "full" cone? If you taper off into infinity (on the mouthpiece end, that is), wouldn't that mean that you would have an unplayable instrument? In other words, doesn't the cone HAVE to have a part that's missing?

* Fourth, do you have any conclusions?

As always, I wish to point out that I have no knowledge of any acoustics, but I find discussions on the topic intriguing.

[MartinMods]

...I find discussions on the topic intriguing.

Intriguing and important......

I get lots of emails from players asking if the Benade Pip will fix their sharp D2-F2 problems. Preliminary screening tests frequently indicate that mouthpiece volume issues are the main cause of the problem. Though the saxophone is a very flexible instrument in this regard, there are limits, and the refined player will reap noticeable benefit from matching his mouthpiece to his instrument optimally.

Just an observation about John's Missing Cone Volume Study results. The debate is still on as to which taper - the neck taper or the body taper, or a length proportional average of the two - most accurately reflects the instrument's volume requirement. John claims that his results, based upon the more acute neck taper angle, match his Classical mouthpiece to within 1%, and that to match the volume requirement based upon the body tube taper angle, the mouthpiece would have to be pulled 3 mm (if I recall correctly ) off the neck cork. I don't wish to debate John's number results here. I only wish to point out, that one does not balance mouthpiece volume requirements by pulling the mouthpiece out or pushing it in. Those are pitch adjustments exclusively. Though they do change the volume, that fact is secondary. Were in fact, more mouthpiece volume required, one would simply use a different mouthpiece design, a wider, fatter chamber combined with throat shape and dimensions which would balance the volume with the Frs pitch requirements, and the mouthpiece would stay firmly on the cork.

[pete]

The debate is still on as to which taper - the neck taper or the body taper, or a length proportional average of the two - most accurately reflects the instrument's volume requirement.Mmmm. I don't understand this. Volume is volume is volume. I can grasp that if you're talking about a sax has to be in a "sax shape" for it to sound like a sax. In other words, if I just stuck a straight length of pipe on an alto that has the same volume as a sax neck, it's not really going to sound all that sax-like. But I think that's confusing the difference (or maybe relationship) of "taper" and "volume".

Were in fact, more mouthpiece volume required, one would simply use a different mouthpiece design, a wider, fatter chamber combined with throat shape and dimensions which would balance the volume with the Frs pitch requirements, and the mouthpiece would stay firmly on the cork. I also don't get this. if you're talking about just adjusting one mouthpiece dimension (bigger chamber, whatever), you're not necessarily changing the volume of the mouthpiece. Am I missing something, there?

BTB, what's an "Frs pitch requirement"?

[jbtsax]

I have a couple questions, too:

* First, wouldn't a straight soprano with a fixed neck be easier to work with, like, a Mark VI? You wouldn't have to worry about the neck as a measurement or any bends.
You are right. A soprano would have been easier. An alto sax was used in the above study to compare the results of using the taper of the neck to define the missing cone with using the different taper of the body to define the missing cone.
* Second, don't the tone holes do something to the overall volume of the cone or is that included in the measurements? That is correct. The effect of the closed toneholes is to make the "acoustic" geometry of the body wider and longer than its physical measurements. This is why I believe that using the physical measurements of the body to define the missing come gives an inaccurate representation.
* Third, do you really want a "full" cone? If you taper off into infinity (on the mouthpiece end, that is), wouldn't that mean that you would have an unplayable instrument? In other words, doesn't the cone HAVE to have a part that's missing?
First of all the "taper" can't go to infinity like parallel lines can. Because they are at an angle they will eventually meet to form the "apex" of the cone. If the saxophone were a complete cone to an apex, there would be nowhere to blow into to make the sound. That is why it is cut off or "truncated". The acoustics of the saxophone are such that the instrument will behave like a completed cone ie. play overtones that are whole number multiples of the fundamental and overblow octaves that are in tune ONLY if the body of the saxophone can be fooled into thinking there is an cone all the way to an apex at the top. The way the saxophone is fooled into thinking the top of its cone isn't missing is when the effective volume* of the saxophone mouthpiece matches that of the "ideal missing cone". The question we have been wrestling with is how to determine the volume and length of the "missing cone" from the known dimensions of the saxophone and its neck.
* Fourth, do you have any conclusions?
My preliminary work points to the conclusion that the missing cone extrapolated from the main body tube is far too large to be a workable choice. Although I will be the first to admit that further study is needed using different size saxophones, and different style mouthpieces. I do believe that a productive approach is to measure the effective mouthpiece volume that works on a given instrument and "reverse engineer" that measurement to try to discover a way to calculate a missing cone volume of similar value. My thinking is that knowing the effective mouthpiece volume that allows the saxophone to play in tune and in tune with itself, by definition, is that volume of the missing cone we are looking for.
As always, I wish to point out that I have no knowledge of any acoustics, but I find discussions on the topic intriguing. I wish to point out that I am not an acoustic scientist, I just play one on woodwind discussion forums. :)

John

* The effective or equivalent volume of the mouthpiece is its geometric volume plus the volume added by the movement of the reed and the effects of the player's embouchure.

[MartinMods]

I don't understand this. Volume is volume is volume.


The saxophone is basically a cone with a bit of the end chopped off. In order for it to work correctly, whatever we stick on the end to make noise with, should have the same internal volume as the part that we chopped off - the mouthpiece (from the end of the neck) + the area that the reed occupies in it's motion + to some extent, the player's vocal tract. This makes the saxophone respond and tune well in the lower frequency resonances - 1st 2 octaves.

Frs: Volume is the first requirement of the substitution. The second is Frs, or (I'm guessing) "frequency of the substitution". The resonance frequency of the mouthpiece + the neck, when played alone, should equal the theoretical frequency of the the theoretical cone having the same length as the part we cut off + the neck. This serves to insure alignment of the higher frequency resonances.

The ratio of the mouthpieces chamber width to it's length, must be within certain parameters for it to be in tune. Not all volume is equal, depending on it's shape and location. You can't take a small chambered mouthpiece and turn it into a large chambered mouthpiece by pulling it off the cork some, as the increase in length will affect the pitch excessively.

[jbtsax]

Frs is frequency of the (oboe) reed on its staple. F - frequency, r - reed, s - staple.

Benade equates this acoustically to the bassoon reed on its bocal, and the saxophone mouthpiece on its neck. He also sometimes refers to the staple, bocal, and neck as the "constriction".

[pete]

First, thank you, gentlemen for answering me/indulging me. As I've said a couple times, I'm fairly interested in the conversation, but I have little to no background in acoustics. It gives me the opportunity to question folks that have more of a clue than me.

Second, thanks to JBT for recognizing that I was thinking of "zero" when I said "infinity". Some of the more interesting hallucinations I'm havening on my current medications are mathematical and I see formulae from my calculus classes I took 20+ years ago with + and - infinity. For some reason I was thinking "infinite zero". Told ya: too many drugs.

My preliminary work points to the conclusion that the missing cone extrapolated from the main body tube is far too large to be a workable choice. Although I will be the first to admit that further study is needed using different size saxophones, and different style mouthpieces. I do believe that a productive approach is to measure the effective mouthpiece volume that works on a given instrument and "reverse engineer" that measurement to try to discover a way to calculate a missing cone volume of similar value. My thinking is that knowing the effective mouthpiece volume that allows the saxophone to play in tune and in tune with itself, by definition, is that volume of the missing cone we are looking for.The way I'm looking at it is that you do have to account for the mouth cavity of the person playing, to some extent. I also still hold out some hope with the theory that there has to be a "missing cone" for the sax to be a sax.

The ratio of the mouthpieces chamber width to it's length, must be within certain parameters for it to be in tune. Not all volume is equal, depending on it's shape and location. You can't take a small chambered mouthpiece and turn it into a large chambered mouthpiece by pulling it off the cork some, as the increase in length will affect the pitch excessively. Again, I'm not getting this. The formula for volume is always the same. However, I get the fact that if you have a mouthpiece that is, say, 12" long and has a chamber of 1", it's not going to play properly. What I'm trying to say is that you can't just completely divorce the volume measurement from the design considerations. Or maybe I'm completely wrong and you could have a 12" x 1" mouthpiece and it's work juuuust fine. Are we talking about the same thing?

[MartinMods]

The formula for volume is always the same.

Yes, but not as far as pitch is concerned. The volume distribution (length, width, tip, throat, must always take into account the varied effect that it will have on the pitch of the mouthpiece.

[pete]

Yes, but not as far as pitch is concerned. The volume distribution (length, width, tip, throat) must always take into account the varied effect that it will have on the pitch of the mouthpiece.
Then I think we're talkin' about the same thing: the mouthpiece must be sax-mouthpiece shaped, but can have some variations and should have a specific volume.

At least, I think so :).

[jbtsax]

I don't agree with everything that has been said about mouthpiece volume. Here is why.

Of course a small chamber mouthpiece will still have the volume and tonal characteristics of a small chamber mouthpiece even when it is pulled farther off the cork and given a larger effective volume. The same is true of a large chamber mouthpiece put farther on to the cork having some of its volume displaced by the neck. The fact is in both cases each retains its tonal characteristics, but the pitch and intonation produced by each changes with the volume added and taken away when the mouthpiece is moved on or off the cork.

I am convinced that it is the volume inside the mouthpiece that determines the pitch and not the length of the instrument measured to the tip of the mouthpiece. Two mouthpiece insert studies were done that show a definite pitch change when the volume inside the mouthpiece is added to or taken away from while the mouthpiece remains in the same position. In the first one Proposition B was found to be the most accurate description.
In the second, actual pitch measurements were taken and recorded.

http://jbtsaxmusic.homestead.com/Neck_insert_study.pdf

http://jbtsaxmusic.homestead.com/Neck_insert_study_text_2.pdf

Of course there are other factors that influence the volume inside the mouthpiece and the pitch as well, such as the hardness (compliance) of the reed, and the player's embouchure.

[pete]

I am convinced that it is the volume inside the mouthpiece that determines the pitch and not the length of the instrument measured to the tip of the mouthpiece
Why can't it be both? Additionally, what would happen with a mouthpiece that has a more conical bore rather than cylindrical?

[MartinMods]

http://jbtsaxmusic.homestead.com/Neck_insert_study.pdf

http://jbtsaxmusic.homestead.com/Neck_insert_study_text_2.pdf



I respectfully disagree with your assessment of the insert, based upon the most essential description of a conical wind instrument, clearly illustrated and explained by A. Benade, on page 21, here:

https://ccrma.stanford.edu/marl/Benade/documents/Benade-Physics323-1977.pdf

A conical wind instrument is a truncated cone and the surrogate for the missing section, consists of 2 parts, a cavity and a constriction of the bore. This can be clearly observed, if we examine the cross section of the most essentially simple, real world saxophone bore - a one piece, straight walled soprano, with an Otto Link STM mouthpiece.

From the mouthpiece end, we clearly see a defined chamber cavity. Our constriction occurs at the neck opening obviously, however, as the bore immediately begins to expand, this real constriction, is effectively lengthless. The truncated conical body section begins where the bore begins to expand. Easy.

Inserting a snug-fitting, 2mm long cylindrical tube, with a neck opening bore diameter, into the throat of the Otto Link, so it snugs up against the neck opening, we reexamine our cross-section.

Once again we have a clearly defined chamber cavity, and a clearly defined constriction - the opening of the insert. As the bore of the insert remains cylindrical, the impedance in the air column in that 2mm section does not change, until we reach the opening of the neck, where the bore begins to expand. Thus the insert can only be seen as a 2mm long constriction, who's length and volume belong to the missing cone surrogate, both physically and acoustically.

Were the bore of the insert conical however, the same slope and diameter as that of the neck or close, then, it would be both a physical and an acoustical extension of the neck.

Pushing the extension up in the throat, towards the mouthpiece tip, causes a double, chamber, double constriction, which Benade claims, does not have much going for it.

[jbtsax]

Quoting Benade Acoustical Evolution of Wind Instruments page 21. next to last paragraph.

CAVITY: it is within the oboe or bassoon reed or sax mouthpiece
CONSTRICTION: it is the oboe reed staple, bassoon bocal, sax neck

It couldn't be stated any more clearly than this..

[MartinMods]

Quoting Benade Acoustical Evolution of Wind Instruments page 21. next to last paragraph.

CAVITY: it is within the oboe or bassoon reed or sax mouthpiece
CONSTRICTION: it is the oboe reed staple, bassoon bocal, sax neck

It couldn't be stated any more clearly than this..

Then please explain my one-piece, straight sided soprano example.

Further, if you accept Benade's statement here, unqualified, then your entire Missing Cone Study is invalid, as the entire neck belongs to the substitution, and the body is truncated at the tenon.

[jbtsax]

It is very simple. The saxophone, like the oboe and bassoon is a woodwind with a conical bore. That conical bore must have the end cut off in order to attach an apparatus to create the soundwave. That apparatus is the saxophone mouthpiece, the oboe reed, or bassoon reed.

There is also a part of the cone that is not missing, but is detachable from the rest of the body of the instrument for practical reasons. That is the staple of the oboe reed, the bocal of the bassoon, and the neck of the saxophone. A notable exception is the older style one piece soprano saxophone that could fit comfortably in a case without a detachable neck. It is this part that Benade also calls the "constriction".

It is impractical if not impossible to analyze the frequency produced by the oboe reed without its staple, the bassoon reed without its bocal or the saxophone mouthpiece without its neck. It is for this reason and this reason only that Benade discusses this combination as an alternate way to view the truncation.

He gives two requirements for a conical woodwind to perform its best acoustically:

1. That the surrogate for the "missing cone" (the oboe reed, the bassoon reed, and the saxophone mouthpiece past the end of the neck) must have an effective volume equal to that of the actual missing cone.

2. That the frequency produced by playing the oboe reed on its staple (Frs), the bassoon reed on its bocal, or the saxophone mouthpiece on its neck match the natural resonant frequency that would be produced by a cone that is the calculated length of the "missing cone" plus the measured length its attachment (staple, bocal, neck) combined. That frequency is found by using the formula:

Frs = V/2 Xo

Frs - Frequency of the oboe reed on its staple, bassoon reed on its bocal, sax mouthpiece on its neck.
V - speed of sound (345 m/s at 74 degrees F)
Xo - calculated length of the missing cone + the length of its attachment.

It is no more complicated than this. The true missing cone is the part beyond the end of the saxophone neck (if it has a neck), the part beyond the end of the staple of the oboe reed, and the part beyond the end of the bassoon's bocal.

The alternate way to describe the missing cone as the reed on its staple, the reed on its bocal, and the mouthpiece on its neck is only to elucidate the above mentioned frequency requirement to make the conical instrument work its best acoustically.

[pete]

Excuse, please, another question: if you're talking about a "straight" conical bore, what happens with the extra bends at the neck and bow of a sax? For that matter, the bocal of a bassoon and the reed of an oboe aren't conical.

As an observation, if the oboe is a true conical-bore instrument, it obviously has a truncated cone: just look at where you're putting the reed.

[jbtsax]

The saxophone neck and bell bow are bends in the conical tube. The acoustic effect as Benade puts it is that the sound wave "sees" a somewhat wider and longer tube as it goes around the bend. The manufacturers compensate (hopefully) by making the bore a bit narrower and shorter to compensate.

The staple of the oboe reed is slightly conical in shape as is the bocal of the bassoon. The oboe is a good visual example of a truncated cone.

[MartinMods]

It is no more complicated than this. The true missing cone is the part beyond the end of the saxophone neck (if it has a neck), the part beyond the end of the staple of the oboe reed, and the part beyond the end of the bassoon's bocal.

I agree, and that is not contradictory to what I posted. Benade's use of "mouthpiece on it's neck" and "....it (the constriction) is the sax neck." is vague, and not to be taken word-for-word. (Though you earlier seemed to imply that it was.) The sax neck is the constriction, but only in that it causes the reduction in bore diameter at it's opening, and nothing more, as my example demonstrates. It is a lengthless constriction, and adding cylindrical length to it, is length added to the substitution, not the neck.

This is demonstrated by the Frs resonance of the mouthpiece/constriction, which exists in the saxophone air column at all times during normal playing. The difference in impedance between the neck opening (constriction) and the expanding neck bore, causes a partial reflection of the wave, back towards the mouthpiece, in the same manner that the wave is reflected back at an open tone hole.

This independent resonance, is responsible for the reed re-opening after closure, and is the reason why the reed closed period = the ratio of the length of the truncation (to the apex) to the length of the truncated body, which means, the reed stays closed only about 25% of the time, compared to about 50%, for the clarinet.

It causes a frequency hole or formant, in the tone produced by the saxophone's normal resonances, which is to a great extent responsible for the characteristic saxophone sound.

It also affects the pitch of normal saxophone tone generating resonances (and these are higher resonances) in it's general area, so if the mouthpiece design considerations (volume, shape, etc) are not correct, and it is sharper or flatter than the theoretical resonance, based on the distance from the apex to it's location, the the surrounding higher resonances will be pulled out of alignment.

There is a little more to it......

[MartinMods]

"It causes a frequency hole or formant"

I mean anti-formant

http://www.acoustics.org/press/151st/Dalmont.html

[jbtsax]

I agree, and that is not contradictory to what I posted. Benade's use of "mouthpiece on it's neck" and "....it (the constriction) is the sax neck." is vague, and not to be taken word-for-word. (Though you earlier seemed to imply that it was.) I read this as saying you know more than Benade on this topic. Given a choice, I think I will go with Benade's interpretation in his published works, if you don't mind. You are of course welcome to your theories built upon your misinterpretation of his use of the term "constriction". I can think of much better uses of my time than to continue a pointless debate on the fine points of your theory about what Benade should have actually said had he not been so vague.

[MartinMods]

I read this as saying you know more than Benade on this topic.

What I can say, without the slightest doubt, is that the example of the one-piece, straight sided soprano, every bit as much a true saxophone as any other, is the clearest demonstration of what a saxophone is, what it's essential mechanical and acoustical parts are, and how Benade's sometimes generalized statements apply. I think anyone can see that.

Once one understands why the mouthpiece/constriction, the substitution, the surrogate missing cone, ...whatever you want to call it.... has it's own resonant frequency, when ON the saxophone body under normal playing conditions, and the influence it has on the other resonances of the complete air column, one can understand Benade's substitution frs requirement, and the insistence, for primarily convenience and mechanical reasons (you can't separate the neck opening from the neck tube) upon the mouthpiece + neck as the testing unit. Testing the frs of the mouthpiece + entire neck is a mere approximation of whether the actual and very real, occurring in the horn under playing conditions, mouthpiece + constriction resonance is the same as it's theoretical, measured from the apex to that point, equivalent. To borrow your original terminology - that is the "True" frs requirement.

All of the post-Benade studies substantiate this, except for yours.

[MartinMods]

Now I have a question about the Mouthpiece Equivalent Volume Study, which you posted this link to above:

http://jbtsaxmusic.homestead.com/mou...lume_study.pdf


It appears to me, that here you made tests with the tube/cork inserted 10mm into the mouthpiece shank exclusively, from which you calculated the actual equivalent volume (reed compliance) added 28% more volume to the hard-walled, mouthpiece chamber, actually used. I think these results are accurate, however, I question your conclusion, that based upon these results at 10mm insertion, you claim that increasing or decreasing the amount of insertion, and therefore mouthpiece volume actually used, that the same 28% increase would apply in every case.

If you made tests with the tube at different insertion lengths, with the same results, then of course, you must be correct. You don't mention any however, and as such, your conclusion would seem scientifically, a bit premature.

I'm inclined to think that, though changing the mouthpiece volume used would have some effect, that to a substantial degree, the reed compliance is fixed, determined by the reed, the lay of the mouthpiece, and the players vocal tract, and independent of the mouthpiece chamber volume.

Let's say we substituted a clarinet tenon-style coupling for the mouthpiece and the tube, and the mouthpiece had the same inner diameter as the tube. What would the added volume be then? It would be 28% of what then, the entire tube volume?

I think this requires more testing before any such absolute conclusion (add 28% in every case - as per your Missing Cone Volume Study) can be made.

[jbtsax]

The more I read the more confused I get. If you don't mind, here are a few questions to provide an opportunity to put down your thoughts and ideas more clearly.

What I can say, without the slightest doubt, is that the example of the one-piece, straight sided soprano, every bit as much a true saxophone as any other, is the clearest demonstration of what a saxophone is, what it's essential mechanical and acoustical parts are, and how Benade's sometimes generalized statements apply. I think anyone can see that.
What exactly does this mean?

Once one understands why the mouthpiece/constriction, the substitution, the surrogate missing cone, ...whatever you want to call it.... has it's own resonant frequency, when ON the saxophone body under normal playing conditions,

Exactly what are you referring to as the mouthpiece/constriction? Is it the mouthpiece plus the constriction that has no length that you keep referring to? What is the "substitution"? Is it just the mouthpiece, or is it the mouthpiece and the neck?

Once you have answered that, please share your understanding of why that has its own resonant frequency when on the saxophone body under normal playing conditions. Also what would that resonant frequency be on an alto saxophone, for example when the note being played is a low C.

. . .and the influence it has on the other resonances of the complete air column, one can understand Benade's substitution frs requirement, and the insistence, for primarily convenience and mechanical reasons (you can't separate the neck opening from the neck tube) upon the mouthpiece + neck as the testing unit.

This quite confusing. I think I know what Benade's "substitution frs requirement is", but what exactly is the influence the Frs of the "whatever" on the other resonances of the complete air column?

Testing the frs of the mouthpiece + entire neck is a mere approximation of whether the actual and very real, occurring in the horn under playing conditions, mouthpiece + constriction resonance is the same as it's theoretical, measured from the apex to that point, equivalent. Again, this statement makes no sense to me. Exactly what point are you trying to get across?

To borrow your original terminology - that is the "True" frs requirement.

Exactly what is the true Frs requirement you are referring to?

All of the post-Benade studies substantiate this, except for yours.
All of the post-Benade studies substantiate what exactly? Which study of mine are you making reference to. I have done several and put them on my website. Can you make a numbered list of all of the information in said study that you believe is in error?

[jbtsax]

Now I have a question about the Mouthpiece Equivalent Volume Study, which you posted this link to above:

http://jbtsaxmusic.homestead.com/mou...lume_study.pdf


It appears to me, that here you made tests with the tube/cork inserted 10mm into the mouthpiece shank exclusively, from which you calculated the actual equivalent volume (reed compliance) added 28% more volume to the hard-walled, mouthpiece chamber, actually used. I think these results are accurate, however, I question your conclusion, that based upon these results at 10mm insertion, you claim that increasing or decreasing the amount of insertion, and therefore mouthpiece volume actually used, that the same 28% increase would apply in every case.

If you made tests with the tube at different insertion lengths, with the same results, then of course, you must be correct. You don't mention any however, and as such, your conclusion would seem scientifically, a bit premature.

I'm inclined to think that, though changing the mouthpiece volume used would have some effect, that to a substantial degree, the reed compliance is fixed, determined by the reed, the lay of the mouthpiece, and the players vocal tract, and independent of the mouthpiece chamber volume.

Let's say we substituted a clarinet tenon-style coupling for the mouthpiece and the tube, and the mouthpiece had the same inner diameter as the tube. What would the added volume be then? It would be 28% of what then, the entire tube volume?

I think this requires more testing before any such absolute conclusion (add 28% in every case - as per your Missing Cone Volume Study) can be made.

Your point is well taken. In that particular study the mouthpiece effective volume was found to be 2.78 ml greater than the physical volume of the mouthpiece used which was an increase of 28%. This was with the mouthpiece only 10 mm on to the cork.

In the comparative missing cone volume study, the mouthpiece was placed 28.2 mm on to the neck. Without doing another mouthpiece effective volume study I had the choice of using the 28% increase or the 2.78 ml increase and I chose the former.

I plan to do another mouthpiece effective volume measurement with the mouthpiece on the cork 28.2 mm and then put that result into the missing cone study. I am also going to use my beaded string device to check the neck length and the graduated cylinder measurement for the mouthpiece volume as well in the interest of accuracy. I will announce when the study with these revisions is posted.

[MartinMods]

Your point is well taken. .....

I plan to do another mouthpiece effective volume measurement with the mouthpiece on the cork 28.2 mm and then put that result into the missing cone study. I am also going to use my beaded string device to check the neck length and the graduated cylinder measurement for the mouthpiece volume as well in the interest of accuracy. I will announce when the study with these revisions is posted.

John,

Thanks. I'll be interested in your results.

I got very accurate mouthpiece volume results using a 30 unit (3/10cc) srynge. I only had to fill it 42 times to get my Bari Richie Cole mouthpiece volume.

Measuring the shortest inside neck length (bottom) and the longest (top, with a slotted rubber insert pressing the solder against the top of the tube it's entire length), the averaged length was 3mm longer than the best center-line measurement I could do by hand.

The correct volume unit for these tests is the cubic centimeter, or cc = 1000mm3. The centi-liter, or cl, is actually 10,000mm3.

[MartinMods]

The more I read the more confused I get.

I think you must empty your cup first.

[jbtsax]

John,The correct volume unit for these tests is the cubic centimeter, or cc = 1000mm3. The centi-liter, or cl, is actually 10,000mm3.

[From Wikipedia] One cubic centimeter corresponds to a volume of 1⁄1,000,000 of a cubic meter, or 1⁄1000 of a litre, or one milliliter; thus, 1 cm3 ≡ 1 mL.

In many scientific fields, the use of cubic centimeters has been replaced by the milliliter.

[jbtsax]

Here is the latest installment in the study of ways to find the frequency requirement to match that of the missing cone.


http://jbtsaxmusic.homestead.com/Calculating_missing_cone_frequency.pdf

[MartinMods]

Here is the latest installment in the study of ways to find the frequency requirement to match that of the missing cone.


http://jbtsaxmusic.homestead.com/Calculating_missing_cone_frequency.pdf

Just from a quick glance, I see that you calculate the frequency of your neck section using the formula for a perfect, straight sided cone, yet in your last neck study, you showed us that your neck was far from anything straight sided, having, according to your measurements, 6 different conical tapers. I see no reference in this latest study to your previous neck measurements, nor any reference to how you treat the 21mm of cylindrical tenon, so clearly diagrammed, which are considered neck length and volume.

In that light, I'm not sure how to interpret the results of this study compared to those previous . There seems to be conflicting information.

[jbtsax]

Just from a quick glance, I see that you calculate the frequency of your neck section using the formula for a perfect, straight sided cone, yet in your last neck study, you showed us that your neck was far from anything straight sided, having, according to your measurements, 6 different conical tapers. I see no reference in this latest study to your previous neck measurements, nor any reference to how you treat the 21mm of cylindrical tenon, so clearly diagrammed, which are considered neck length and volume. In that light, I'm not sure how to interpret the results of this study compared to those previous . There seems to be conflicting information.

Please try to understand my response to your questions so we don't get into another circular argument like before.

1. The natural resonant frequency of the fundamental is based upon the length of a cone x 2 or the length of a cylinder x 4. The taper of the cone or its irregularity only affects the modes above the fundamental. F = c/2L applies whether the cone is perfectly straight sided or not.

2. The 21 mm tenon of the neck is a part of the neck's length that determines the length of the soundwave and therefore the frequency.

3. There is no conflicting information if one understands the principles underlying the calculations used in each study.

[MartinMods]

John,

Thanks. I was unaware that the formula for the frequency of a perfect cone also applied to non-cone shapes. Following your method, I measured my unaltered Martin tenor neck (211.41mm), center-line, tip to tip, and calculated it's theoretical frequency (818.29Hz). Then I stopped the tenon end (flat across the open end) and tested it's actual frequency by both popping and blowing across the small end. The neck produced a perfectly in-tune concert Ab (830.64Hz). That's a difference of 25 cents. That is certainly not good enough for musical intonation. Is that close enough for frs tuning? It would appear that those missing ca. 3 ml do make a difference.

Lance
MM

[MartinMods]

Sorry, I made a mistake. No transposition necessary, so the actual pitch generated by my tenor neck was a perfectly in-tune concert Bb (932.32Hz) and that's a difference of 226 cents ( 2 semi-tones and 26 cents).

[MartinMods]

John,

I just tested my Martin alto neck (tenon removed) via your method.

Length: 169.86mm
Played Frequency (stopped and popped/blown): 1480hz
Calculated (by length F = 346m/169.86mm*2: 1018.47Hz

Lance

[jbtsax]

This is great Lance! You always force me to go do some more research. Here is the answer to the conundrum you have presented from Wikipedia at this link:

http://en.wikipedia.org/wiki/Acoustic_resonance

Cones

An open conical tube, that is, one in the shape of a frustum of a cone with both ends open, will have resonant frequencies approximately equal to those of an open cylindrical pipe of the same length. Open cylindrical tubes resonate at the approximate frequencies

f = v/2L v=speed of sound

The resonant frequencies of a stopped conical tube — a complete cone or frustum with one end closed — satisfy a more complicated condition:

kL = nπ − tan − 1kx where the wavenumber k is k = 2πf / v

What is happening then is that you are creating a closed cone by the manner you are generating the sound. When the mouthpiece is on the cork and played on the neck, the neck is an open frustum which behaves much like an open cylinder as far as resonant frequency is concerned. I have been trying to find a way to get a stable resonant frequency from my alto neck with both ends open with little or no success. I was able to get the calculated frequency one time, but have been unable to recreate striking it in exactly the same manner to repeat the result. If you find a way, please let me know.

John

[MartinMods]

John,

No problem. The open tube is the same as a flute or recorder, so just blow across the small end, and you will hear the pitch. It doesn't form a strong regime. Actually, it's very weak, but you can hear a definite pitch. It's the same, blowing on the large end, though even softer. Don't forget to plug the register hole.

The played pitch of my alto neck was 932Hz. The calculated pitch was 1018Hz. That's a difference of 153 cents, or, a half step + quarter tone.

Lance

[jbtsax]

John,

No problem. The open tube is the same as a flute or recorder, so just blow across the small end, and you will hear the pitch. It doesn't form a strong regime. Actually, it's very weak, but you can hear a definite pitch. It's the same, blowing on the large end, though even softer. Don't forget to plug the register hole.

The played pitch of my alto neck was 932Hz. The calculated pitch was 1018Hz. That's a difference of 153 cents, or, a half step + quarter tone.

Lance

I'm curious as to how your are measuring the Frequency of your played note so exactly.

Also how is it you are getting the same blown pitch with both ends open as before with one end closed. That does not correlate with the information in the link I provided.

A truncated cone open on both ends behaves much like an open cylinder. A closed cone has a much different formula to find its pitch. I believe it is safe to assume that pitch is not the same as a cone open on both ends. Yet your "blowing" test both open and closed revealed the exact same pitch. What's up with that, as Jerry Seinfeld would say? :)

[pete]

No soup for you!

[MartinMods]

I'm curious as to how your are measuring the Frequency of your played note so exactly.

I have 2 methods.

1. Blowing the neck while simultaneously playing a digital keyboard. Remarkably, in these cases, the played pitch has been either a perfect unison or within a few slow beats of a perfect unison. Changing blowing angle does not influence the pitch appreciably.

2. A digital tuner with digital and analog read-out.

Also how is it you are getting the same blown pitch with both ends open as before with one end closed. What's up with that, as Jerry Seinfeld would say?

What's up with that is, it pays to read the information slowly and carefully. You are confused. So what would Jerry say then?

The alto neck was first play tested as a closed frustum (1480Hz) and calculated using the open cone formula, as having a calculated frequency, by length F = 346m/169.86mm*2, of 1018.47Hz. As you pointed out, the neck should be play tested as an open cone.

The second play test of the same alto neck, as an open cone, and tested from each open end, resulted in a frequency of 932Hz. Again, the same neck calculations using the open cone formula, as having a calculated frequency, by length F = 346m/169.86mm*2, of 1018.47Hz.

There are no errors in the second test. The difference between the tested and calculated, open cone frequencies was 153 cents, or, a half step + quarter tone.

Do not confuse the tenor neck test results with those of the alto neck. If you doubt the integrity of my numbers, I suggest you play test your own neck as an open cone. It's quite simple. Just put your lips together and blow.

[jbtsax]

My mistake. You first used the tenor neck unaltered stopped and then switched to the alto neck without a tenon stopped. Then you changed to the alto neck unstopped. It was kind of like a sax neck shell game. :)

I did actually mistake the alto result for one of the tenor results. I will certainly read more carefully next time.

Does your digital tuner give the reading in Hz or in cents?

I can't imagine that airy sound from blowing across the end of the neck making audible out of tune "beats" with another fixed pitch. Are you sure about that?

Is there any chance you could record the sound you get to an MP3 file so I can run it through my frequency analysis software? I would like to see if that gives the same exact pitch.

I guess "no soup for me". Sorry for the "honest" mistake.

John

[MartinMods]

My mistake. You first used the tenor neck unaltered stopped and then switched to the alto neck without a tenon stopped. Then you changed to the alto neck unstopped. It was kind of like a sax neck shell game. :)

Not really. The alto information was in a different posting than the tenor information, and each posting was clearly designated with, "I measured my unaltered Martin tenor neck (211.41mm)", or, "I just tested my Martin alto neck (tenon removed) via your method. Length: 169.86mm". If that's a shell game, let's start betting money.

I can't imagine that airy sound from blowing across the end of the neck making audible out of tune "beats" with another fixed pitch. Are you sure about that?John

You must wear headphones.

It's thought that the average person can distinguish pitch differences of 10 cents. A trained musician should be able to reach the limit of around 4.3 cents - http://www.absoluteastronomy.com/topics/Pitch_%28music%29

Here's an interesting hearing test:

http://audiocheck.net/blindtests_pitch.php?cent=50

I have a trained ear, both as a musician and a recording engineer, so I can tell if 2 sequential tones are perfectly in tune, close and will beat slightly, or too out of tune for musical use. I'll see if I can make a recording of both sounds together, so you can maybe hear what I hear, if you really think that is necessary.

I really suggest that you try to use your ears first when doing your own testing. You can also hear the pitch of your neck by holding the small end 1" from your ear, and tapping the side of the tenon with your finger. If you cover 1/4 of the large end, the pitch will drop about 100 cents. Alternate between open and partially closed to see if you can hear a difference.

[MartinMods]

I'll try to record some samples and filter out the noise.

You could use an adjustable oscillator and tune it to match the played frequency, as best you can by ear. That should be good enough.

[jbtsax]

How about that MP3 recoring of your played pitch to see whether you are blowing air or just smoke?

[MartinMods]

I really don't need your insults, smiley face or not. How about that MP3 recoring of your played pitch to see whether you are blowing air or just smoke?

No insult intended. Just a matter-of-fact, test your own neck by blowing on it or tapping on it. If you can't hear the pitch, even enough to tell if you are in the ball park, you can't hear the pitch. If that insults you, well, too bad. They are your ears, not mine.

[jbtsax]

No insult intended. Just a matter-of-fact, test your own neck by blowing on it or tapping on it. If you can't hear the pitch, even enough to tell if you are in the ball park, you can't hear the pitch. If that insults you, well, too bad. They are your ears, not mine.Ball park doesn't quite measure up when you are using a formula to find the exact frequency in Hz based upon the wavelength. How about some sound files to demonstrate what you are saying is true? That is the question on the table, not how good my ears are.

[MartinMods]

Ball park doesn't quite measure up when you are using a formula to find the exact frequency in Hz based upon the wavelength.

If I have time to make a recording, I will, but I really don't feel obligated to do so. I can clearly hear that the pitch is over a semi-tone off, from the calculated frequency, so I thought I would help you out with that information. That much should suffice, I think. It certainly put the issue to rest in my mind. If you need more proof than that this second, you will have to do your own testing. Or you can just discount my postings. I don't care.

[jbtsax]

If I have time to make a recording, I will, but I really don't feel obligated to do so. I can clearly hear that the pitch is over a semi-tone off, from the calculated frequency, so I thought I would help you out with that information. That much should suffice, I think. It certainly put the issue to rest in my mind. If you need more proof than that this second, you will have to do your own testing. Or you can just discount my postings. I don't care.
Thanks Lance. That certainly answers my question. I have done my own testing and have posted the results on the mouthpiece forum. By adding an end correction I found a good agreement with the "airy tone" pitch given by my Korg tuner and the calculated frequency of the open ended neck. I am going to try to recreate that with the neck from my Yomama Custom tenor. I will keep you posted.